Fourier series: Differentiation and integration of Fourier series
Differentiation of Fourier series
Let #f# be the function defined by setting #f(x)=9\cdot \left| x\right| # for #x\in \ivco{-\pi}{\pi}# and extending it by #2\pi#-periodicity to the whole real line. Select, among the options given below, the Fourier series of \(f' \) knowing that the Fourier series #s# of #f# is given by \[ \displaystyle s(x) = {{9\cdot \pi}\over{2}} + {{36}\over{\pi}}\sum_{n=1}^{\infty} \frac{\cos((2n-1)x)}{(2n-1)^2}\]
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